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- W4297945101 abstract "We prove a version of the Cauchy-Davenport theorem for general linear maps. For subsets $A,B$ of the finite field $mathbb{F}_p$, the classical Cauchy-Davenport theorem gives a lower bound for the size of the sumset $A+B$ in terms of the sizes of the sets $A$ and $B$. Our theorem considers a general linear map $L: mathbb{F}_p^n to mathbb{F}_p^m$, and subsets $A_1, ldots, A_n subseteq mathbb{F}_p$, and gives a lower bound on the size of $L(A_1 times A_2 times ldots times A_n)$ in terms of the sizes of the sets $A_1, ldots, A_n$. Our proof uses Alon's Combinatorial Nullstellensatz and a variation of the polynomial method." @default.
- W4297945101 created "2022-10-01" @default.
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- W4297945101 date "2015-08-09" @default.
- W4297945101 modified "2023-09-26" @default.
- W4297945101 title "A Cauchy-Davenport theorem for linear maps" @default.
- W4297945101 doi "https://doi.org/10.48550/arxiv.1508.02100" @default.
- W4297945101 hasPublicationYear "2015" @default.
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